Question

If \(\vec{n}_1\), \(\vec{n}_2\), and \(\vec{i}\) represent unit vectors along the incident ray, reflected ray, and normal to the surface, respectively, then:

• A. \(\vec{n}_2 = \vec{n}_1 - 2(\vec{n}_1 \cdot \hat{t})\hat{t}\)
• B. \(\vec{n}_2 = \vec{n}_1 + 2(\vec{n}_1 \cdot \hat{t})\hat{t}\)
• C. \(\vec{n}_2 = -\vec{n}_1\)
• D. \(\vec{n}_2 = 2\vec{n}_1 - (\vec{n}_1 \times \hat{t})\)

Hint:

The law of reflection states that the angle of incidence equals the angle of reflection. In vector form, this can be represented using the normal vector andthe dot product for the direction of the reflected ray.

Answer 1

The Correct Option is B

1. Step 1: According to the laws of reflection, the incident ray, the reflected ray, and the normal to the surface all lie in the same plane, and the angle of incidence equals the angle of reflection.
2. Step 2: Using the vector representation of reflection, we have:\[ \vec{n}_2 = \vec{n}_1 + 2(\vec{n}_1 \cdot \hat{t})\hat{t} \]
This is the correct vector equation for the reflected ray direction based on the law of reflection.